rbox(1)
NAME
rbox - generate point distributions for qhull
SYNOPSIS
Command "rbox" (w/o arguments) lists the options.
DESCRIPTION
rbox generates random or regular points according to the options given,
and outputs the points to stdout. The points are generated in a cube,
unless 's' or 'k' option is given. The format of the output is the
following: first line contains the dimension and a comment, second line
contains the number of points, and the following lines contain the
points, one point per line. Points are represented by their coordinate
values.
EXAMPLES
- rbox 10
- 10 random points in the unit cube centered at the origin.
- rbox 10 s D2
- 10 random points on a 2-d circle.
- rbox 100 W0
- 100 random points on the surface of a cube.
- rbox 1000 s D4
- 1000 random points on a 4-d sphere.
- rbox c D5 O0.5
- a 5-d hypercube with one corner at the origin.
- rbox d D10
- a 10-d diamond.
- rbox x 1000 r W0
- 100 random points on the surface of a fixed simplex
- rbox y D12
- a 12-d simplex.
- rbox l 10
- 10 random points along a spiral
- rbox l 10 r
- 10 regular points along a spiral plus two end points
- rbox 1000 L10000 D4 s
- 1000 random points on the surface of a narrow lens.
- rbox c G2 d G3
- a cube with coordinates +2/-2 and a diamond with coordinates +3/-3.
- rbox 64 M3,4 z
- a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lattice (Mesh) of integer points. 'rbox 64 M1,0' is orthogonal.
- rbox P0 P0 P0 P0 P0
- 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'.
- r 100 s Z1 G0.1
- two cospherical 100-gons plus another cospherical point.
- 100 s Z1
- a cone of points.
- 100 s Z1e-7
- a narrow cone of points with many precision errors.
OPTIONS
n number of points
Dn dimension n-d (default 3-d)
Bn bounding box coordinates (default 0.5)
l spiral distribution, available only in 3-d
- Ln lens distribution of radius n. May be used with 's', 'r', 'G',
- and 'W'.
- Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0], [0,0,r], ...}.
- Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}. '27 M3,4 z' is a rotated integer lattice.
- s cospherical points randomly generated in a cube and projected to
- the unit sphere
- x simplicial distribution. It is fixed for option 'r'. May be
- used with 'W'.
- y simplicial distribution plus a simplex. Both 'x' and 'y' gener
- ate the same points.
- Wn restrict points to distance n of the surface of a sphere or a
- cube
- c add a unit cube to the output
- c Gm add a cube with all combinations of +m and -m to the output
- d add a unit diamond to the output.
- d Gm add a diamond made of 0, +m and -m to the output
- Pn,m,r add point [n,m,r] to the output first. Pad coordinates with
- 0.0.
- n Remove the command line from the first line of output.
- On offset the data by adding n to each coordinate.
- t use time in seconds as the random number seed (default is com
- mand line).
- tn set the random number seed to n.
- z generate integer coordinates. Use 'Bn' to change the range.
- The default is 'B1e6' for six-digit coordinates. In R^4, sevendigit coordinates will overflow hyperplane normalization.
- Zn s restrict points to a disk about the z+ axis and the sphere
- (default Z1.0). Includes the opposite pole. 'Z1e-6' generates degenerate points under single precision.
- Zn Gm s
- same as Zn with an empty center (default G0.5).
- r s D2 generate a regular polygon
- r s Z1 G0.1
- generate a regular cone
BUGS
Some combinations of arguments generate odd results.
Report bugs to qhull_bug@qhull.org, other correspondence to
qhull@qhull.org
SEE ALSO
AUTHOR
- C. Bradford Barber
c/o The Geometry Center
400 Lind Hall
207 Church Street S.E.
Minneapolis, MN 55455